Final answer:
To solve -5n + 7 - 5n = -9 - 10n + 16, combine like terms on both sides of the equation and simplify to find that the equation has infinitely many solutions.
Step-by-step explanation:
To solve the equation -5n + 7 - 5n = -9 - 10n + 16, we can start by combining like terms on both sides of the equation. This gives us -10n + 7 = -10n + 7.
Now, we can subtract -10n from both sides of the equation to simplify further.
This leaves us with 7 = 7.
Since 7 equals 7, the equation is true for all values of n.
Therefore, it has infinitely many solutions, and the correct answer is C.
Infinitely many solutions.